Question

Perform the indicated operation & simplify. Express the answer in terms of i (as a complex number).
-5i(11+3i)=

Answer 1

To perform the operation \(-5i(11 + 3i)\), we distribute \(-5i\) to both terms inside the parentheses:

\[
-5i \cdot 11 + (-5i) \cdot (3i)
\]

Calculating each term separately:

1. For the first term:
\[
-5i \cdot 11 = -55i
\]

2. For the second term:
\[
-5i \cdot 3i = -15i^2
\]
Since \(i^2 = -1\), we can substitute:
\[
-15i^2 = -15(-1) = 15
\]

Now, putting both results together, we combine the terms:

\[
-55i + 15
\]

To express this in standard form (a + bi), we write:

\[
15 - 55i
\]

Thus, the simplified expression is:

\[
\boxed{15 - 55i}
\]